Problem: Given $ m \angle CBD = 5x + 39$, and $ m \angle ABC = 9x - 125$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Solution: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {9x - 125} + {5x + 39} = {180}$ Combine like terms: $ 14x - 86 = 180$ Add $86$ to both sides: $ 14x = 266$ Divide both sides by $14$ to find $x$ $ x = 19$ Substitute $19$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 5({19}) + 39$ Simplify: $ {m\angle CBD = 95 + 39}$ So ${m\angle CBD = 134}$.